Projective Synchronization Of Uncertain Fractional Chaotic Systems

Chaos is a kind of special state behavior in nonlinear dynamical systems.Its phenomena are commonly found in the natural sciences and social sciences and have attracted much attention and attention from researchers in fields including mathematics and control.Chaotic system has the characteristics of extreme sensitivity to initial value and parameter variables,no periodicity and long-term unpredictability.It can be used in many fields such as image encryption and secure communication.Therefore,effective synchronization control is an important part of chaos application.As the theory of fractional calculus becomes more and more perfect,further explorations of chaotic systems have also gone deep into the fractional order.In fact,through the use of fractional differential operators,it is found that the constructed physical chaos system not only possesses all the dynamic behavior of an integer order chaotic system,but also has a more comprehensive description and can reveal the essence of objective problems.At present,great breakthroughs have also been made in the application of fractional-order chaos systems in areas such as information security and control engineering.Therefore,the research on the synchronization control of fractional-order chaotic system has very important theoretical significance and engineering practical value.In this paper,we propose a new method for the synchronization control of uncertain fractional-order chaotic systems,and carry out in-depth analysis and discussion of the existing problems.At the same time,we adopt effective scientific proofs and numerical verification methods to verify the effectiveness of proposed new scheme.The main contents and results of this paper are as follows:1.The synchronization of a class of uncertain fractional-order chaotic systems with dead-time nonlinear input and external disturbances is studied.A synchronization scheme based on fuzzy neural network and adaptive sliding mode control is designed.Using the theory of fractional order Barbalat lemma and fractional stability,this control scheme is theoretically analyzed.Numerical simulations verify the feasibility of the proposed control scheme.2.Based on fuzzy control theory,sliding mode control theory and adaptive control theory,the problem of mixed projection synchronization for a class of uncertain fractional-order chaotic systems with external disturbances is studied.The fuzzy logic system is used to approximate the unknown nonlinear function and external perturbation.At the same time,a kind of fractional-order integral sliding surface with strong robustness is constructed.Then a suitable controller is designed.Numerical experiments show that this control method can realize the hybrid projection synchronization of uncertain fractional-order chaotic systems.3.The projection synchronization problem of fractional-order chaotic systems is studied.Based on Takagi-Sugeno(T-S)fuzzy model and predictive feedback control,a new projection synchronization control scheme is proposed.Using the fractional Lyapunov analysis method,the criteria for realizing projective synchronization of fractional-order chaotic systems are deduced.The effectiveness of the scheme is further verified by numerical simulation experiments on two different fractional-order chaotic systems.